Wanted: Cycles "Shadow Only" Lamp - Not a simple "shadow catcher" question
Use two different render layers

Put the "lamp" on a separate layer and Exclude that layer from the render by clicking on the corrisponent box in the Layer panel.

Your scene now should be affected only by the environment's light (and eventually other light sources, but not the mentioned "lamp").



In the second render layer, uncheck the Use Environment box to remove world's shader influence. The result is a scene lit by the lamp only. Enable this this time the Shadow pass in order to acquire the info about where the shadow fall.



Finish by color mixing the Composite pass from the first render layer with the Shadow pass from the second with Multiply option. Use the Factor slider to adjust the influence of the lamp's shadow in the final image